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Novel closed-form equation for oscillation frequency range of differential ring oscillator

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Abstract

In this article, a novel efficient circuit level analysis is proposed for the oscillation frequency in the differential ring oscillator with N-stage, where N is larger than 3, and exact closed-form equations are achieved for the oscillation frequency range and average oscillation frequency (\( f_{av} \)). In order to attain the maximum oscillation frequency until the drain current of MOSFET is a square-wave, it is assumed which transistors are switching. At first, the amplitude of each harmonic of the output voltage is calculated by Fourier series expansion. Then, by some simplifications, the oscillation frequency range and \( f_{av} \) are derived in the closed-form equations. Comparatively, the time and frequency domain analyses have been dominantly employed for the previous and the proposed works, respectively. There is an excellent agreement among experimental, simulation and theoretical results.

Keywords

Analytical equation Circuit analysis Closed-form equation Differential ring oscillator Oscillation frequency range VCO 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringBabol Noshirvani University of TechnologyBabolIran

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